Method for measurement of scatter and absorption of light

ABSTRACT

The transmission, reflectivity, and loss characteristics of mirrors is determined by a method and apparatus employing several mirrors whose transmission characteristics are measured individually and in series. The use of a pair of like mirrors simplifies the method and minimizes the amount of computer time needed to conduct the process for determining mirror reflectivity and loss. The absorbed component of total loss is found by determining loss at zero spacing of a pair of mirrors by extrapolation from measurements made when the mirrors were spaced. For the most part, the method is arranged so that the computations may be made by hand rather than by computer, if desired.

United States Patent Hansen Sept. 5, 1972 Inventor: Dale II. Hansen,6442 Langford Circle, Huntington Beach, Calif. 92647 Filed: Oct. 19,1970 Appl. No.: 81,660

References Cited OTHER PUBLICATIONS (599100001) Norbury, A. H.Reflectance Spectroscopy and its Applications In Lab. Pract. 18(7): p.754- 9, July 1969 (500450008) Mallett, J. F. W. et al. A LogarithmicAnalog to Digital Converter Used for Optical Density, Measurements inSci. Instrum. 3(3): Mar. 1970 Primary Examiner-Eugene G. Botz AssistantExaminer--R. Stephen Didine, Jr. Attorney-Nienow & Frater [57] ABSTRACTThe transmission, reflectivity, and loss characteristics of mirrors isdetermined by a method and apparatus employing several mirrors whosetransmission characteristics are measured individually and in series.The use of a pair of like mirrors simplifies the method and minimizesthe amount of computer time needed to conduct the process fordetermining mirror reflectivity and loss. The absorbed component oftotal loss is found by determining loss at zero spacing of a pair ofmirrors by extrapolation from measurements made when the mirrors werespaced. For the most part, the method is arranged so that thecomputations may be made by hand rather than by computer, if desired.

10 Claims, 14 Drawing Figures P a cb I02 I04 Q T) O I22 I 6 120 I24 Ocriznzm t l I00 I PLOTTER u4 DATA PROGRAM COMPUTER STORAGE I08 DISPLAYPATENTEDSEP 1912 3.689.746

SHEET 1 BF 5 acb IO4\O I 1 PLOTTER \n4 DATA PROGRAM COMPUTER STORAGE n2no I08) DISPLAY Ra P INVENTOR fiEE DALE H. HANSEN flaw f $41;

ATTORNEYS PATENTEDSEP 5 IIII2 3.689.746

SHEET 2 F 5 MEASURE TRANSMISSION 42p MEASURE TRANSMISSION SI I= Tab FROMT21 Tb Tab x to x 2O 22 24 44 STORE STORE STORE PLOT AND I T J Tb JEXTRAPOLATE a Tab To d=o SOLvE FOR SOLUTION STORE AvERASE PROGRAM IOO Tab SO 28 5O SOLUTION STORE SOLUTION PROGRAM 200 b PROGRAM 5001 S2 SOLvEFOR v a 4b Ra Rb II'IT STORE STORE STORE STORE o a o b L Ra Rb S4 SS SS40 SOLUTION SOLvE FOR PROGRAM 400 o a b figj STORE STORE 'NVENTOR 6O (X(Xb 62 DALE H. HANSEN AT TO RNEYS PATENTEDSEP 5 1912 3,689,746

SHEET 3 [1F 5 STORE STORE STORE SOLVE FOR SOLUTION PROGRAM 500 STORESTORE STORE (x a O( b d C "STORE] STORE SURE Ra Rb Tabc Tc STORE STORESTORE STORE Ta Tb Tc Tab; 20 22 92 94 SOLVE FOR SOLUTION is j a PROGRAM600 96 STORE INVENTOR DALE H. HANSEN ATTORNEYS PATENTED 19 2 3.689.748

SHEET 5 0F 5 v INVENTOR DALE H. HANSEN ATTORNEYS METHOD FOR MEASUREMENTOF SCATTER AND ABSORPTION OF LIGHT This invention relates to methods andmeans for determining losses in mirrors.

The optical characteristic of a mirror is defined by specifying whatportion of incident light is transmitted through the mirror, whatportion is reflected by it, and what portion is lost by absorption andwhat portion is lost by scattering. While the transmissivity of a mirroris readily determined by direct measurement, reflectivity is less easilymeasured and is best measured indirectly. Loss cannot be measureddirectly. It is an object of the invention to provide a means by whichreflectivity and losses, both absorptive and scattering losses, can beaccurately determined. Another object is to provide a method by whichthose characteristics may be determined automatically in a preprogrammedcomputer system whereby mirrors can be accurately, rapidly, andinexpensively characterized and evaluated and inspected.

It is a specific object of the invention to provide a method which canutilize high speed electronic and mechanical computing devices. Thisobject is realized, and it is possible to practice the invention, usingexisting computers both of the analog and the digital types. However,the rate of mirror production and the need for evaluation may not besufficiently great to warrant devoting a computer exclusively topracticing the method. Accordingly, another object of the invention isto provide a method in which the computing steps may be accomplishedafter, rather than intermediate to, those steps which require testingand manipulation of the test mirrors. While automatic computation in apreprogrammed computer is preferred, one of the advantages of theinvention is that the computations can be made by hand in the absence ofa computer or to verify that the computer is performing accurately.

These and other objects and advantages of the invention, which willhereinafter appear, are realized by a provision of a method in which thetransmission characteristics of two or more mirrors are measuredindividually and in pairs. These measurements are introduced into thecomputer along with the controlling program. The computer accomplishesthe computation according to that program, utilizing the inputinformation, and it provides an output which describes the losscharacteristics and the reflectivity characteristics of the mirror, orat least one of those characteristics.

The method requires measurement only of the transmission characteristicsof the mirrors singly and in series. In certain instances it requiresmeasurement of the separation between the coated surfaces of themirrors. Certain of these measurements can be made simultaneously withthe computation. However, all of them may be made prior to thecomputation and the results of measurement stored and subsequentlyintroduced into the computing step.

In the drawings:

FIG. 1 is a schematic diagram of an apparatus embodying the inventionwhich is capable of measuring the transmission characteristic of mirrorsindividually or in series, of storing those measurements, of plottingmeasured data and extrapolating curves, of making computations accordingto a control program, and of displaying the results of thosecomputations;

FIG. 2 is a diagram illustrating the paths of light rays through a pairof mirrors in series;

FIG. 3 is a flow diagram illustrating how the average value of loss fora pair of mirrors is determined and how the reflectivity and loss in apair of similar mirrors is determined.

FIG. 4 is a diagram illustrating how the specific loss for three mirrorsis specified when the average loss for the mirrors in pairs has beenspecified as by the method illustrated in FIG. 3;

FIG. 5 is a diagram illustrating the steps in computing the loss of athird mirror if the transmission and reflectivity characteristics of twoother mirrors are known; and FIGS. 6 through 11 are diagrams of solutionprograms employed to accomplish computations in the method by hand ormechanically, using mechanical or electronic digital or analog computingapparatus.

FIGS. 12, 13 and 14 are diagrams depicting how a light ray istransmitted and reflected by each pair of mirrors in a system of threemirrors in tandem.

The law of conservation of energy may be written:

in which 1 indicates impingement of a unit quantity of light upon amirror, T is the decimal part of thatunit quantity of light that istransmitted through the mirror, R is the decimal part of that unitquantity of light that is reflected from the mirror, and a is thatdecimal part of the unit quantity of light which is lost by absorptionand/or by scattering. In the discussion that follows, a denotes thatportion of loss that is accounted for by absorption. The symbol a, meansloss due to scattering. Examples of the invention will involve the useof three mirrors designated a, b and c. The transmission characteristicsof these three mirrors are designated by the symbols T,, T,, and Trespectively. The reflectivity of those three mirrors is represented bythe symbols R,,, R,, and R respectively. Similarly, the total loss inthose several mirrors is designated a a,,, and a respectively. Theabsorptive loss in mirror a is designated a,,. The scatter loss inmirror b is given by the symbol a The transmission through the seriescombination of mirrors a and b is represented by the symbol T,,,,. Thesymbols applicable to the other mirrors and mirror pairs can be found byanalogy. I

The interrelationship between the variables, in the mathematicalexpressions that define the optical characteristics of mirrors, is notcomplex and is easily within the capabilities of existing computers tocalculate completely and accurately. Computer technicians andprogrammers are easily capable of constructing and operating computersto solve expressions of the relationships which are developed in thefollowing paragraphs. The ability of those computers to makecomputations according to a prearranged solution program is coupled inthe invention with preparing that program in a form that requires theintroduction only of accurately measurable data using mirrors which aresubstantially identical in physical characteristics and, therefore, intheir optical characteristics.

Referring to FIG. 2, if a unit quantity of light is transmitted fromsource P as a ray which impinges upon mirror 10, passing through itssubstrate 12 to its reflective coating 0, a portion T will betransmitted through the reflective coating a and a portion R, will bereflected from it. The transmitted portion T proceeds until it impingesupon the reflective coating b of mirror 14. A portion of the transmittedT,, of the ray is transmitted in part through the reflective coating bto pass through the substrate 16 and out of the mirror 14. Another partof the transmitted portion T of the original a ray will be reflectedfrom coating b, and that part is designated T R As illustrated in FIG.2, the original ray is partly reflected and partly transmitted at itsfirst intersection with the mirror coating. The reflected portion iseither transmitted or reflected. That portion that is reflected isreflected in part and transmitted in part, the reflected part itselfbeing reflected or transmitted at the next intersection. That process isrepeated until the quantity of light remaining after many reflections isso small as to be insignificant in the computation. The quantity oflight at each reflection and transmission is expressed mathematically inFIG. 2. All of the light that passes through the second mirror iscollected and gathered at point X. That portion of the original unitquantity of light T that arrives at point X is designated T Thatquantity of light that would arrive at point X if the mirror 14 wasremoved is designated T That quantity of light which would arrive atpoint X if the mirror 10 was removed, without removal of mirror 14, isdesignated T The quantities T T and T,,,, are easily measured using anoptical bench as illustrated in FIG. 1.

The invention makes use of the solution program expressions of FIGS. 6through 11. Their accuracy is demonstrated in the following developmentAn expression for the quantity of light T,,,, can be found by adding thelight emanating from the second mirror in FIG. 2. That expression isgiven as follows:

T Ta Tb+ Ta Tb Ra Rb+ Ta Tb Ra Rb Ta Tb Ra Rb Ta Tb R R Serial No.81,660

EXHIBIT A Define: T (T T W and R, (R R As n approaches infinity, T T (lR Substitute R l T 01,.

Applying the binomial theorem: (T (I 1 i l T, T The positive of theradical describes a condition which is physically impossible. Thenegative radical is chosen.

Solving: a 1 T,,-( l- T T Substituting (T,,T,,)" T,

where represents the loss expressed in terms of transmission andreflection in each of two like mirrors in tandem.

EXHIBIT A The general form of this expression is written a 1 1 2) in 12)where 0: is the average loss for the two mirrors. and this expression isdefined as solution program 100 in FIG. 6.

Measurement of the transmission of light through the mirrorsindividually and in series will yield accurate transmission data if themirrors are placed so that the reflective coatings face one another andif the substrates are reasonably clean and clear with parallel faces.The assumption that the optical characteristics of the two mirrors aresubstantially identical can be made without material error if themirrors are substantially identical in their physical dimensions and ifthe substrates were made at the same time or under like conditions andif they were coated in the same process. The separation between themirrors when they are measured in series should be at least severalwavelengths as indicated by the symbol D X Referring to the method ofFIG. 3, the quantities T and T and T are measured in step 18. T ismeasured at mirror separation equal to X which means a distance greaterthan a few wavelengths. The measurements are made and the results arestored as indicated at blocks 20, 22 and 24 in FIG. 4. Next, acomputation is made to find the average loss for the two mirrors, a andb. This is done in a step designated 26 in a computer which utilizes theinformation Ta, Tb and Tab and is controlled in step 25 by a solutionprogram 100. The solution found by the computer is stored, as indicatedby block 28, as the loss crab. Using the same computer, or another, acomputation is made as indicated by block 30 for the loss in theindividual mirrors, and for reflectivity in the individual mirrors. Thecomputation is made utilizing the stored information at blocks 20, 22and 28 and by controlling the computer at block 32 with the solutionprogram 200 which is shown in FIG. 7.

Since the average loss for the two mirrors is a 12 or a one and sincethe two mirrors are assumed to have like optical properties, a l a 2 aave and from the conservation of energy law R1 l T1 al.

The output of the computation step 32 is stored as indicated in blocks34, 36, 38 and 40. The transmission, reflectivity, and loss in thecoating a are identified in blocks 20, 38 and 34, respectively. Theoptical characteristics transmission, reflectivity, and loss of thecoating b, are stored in blocks 22, 40 and 36, respectively.

It remains to separate the loss into its absorbed and scatteredcomponents The scattered light is lost by being walked" by multiplereflections out of the space between the two mirrors. The amount of thatloss is reduced as the spacing between the mirrors is reduced. Itbecomes zero when the spacing between the mirrors is absolutely zero.This condition is difficult to reach physically but data, taken atdifferent degree of mirror separation near the point of zero separation,can be extrapolated to find the zero separation loss. That loss ispresumably entirely loss by absorption. Substrating that loss from totalloss provides the value of loss by scatter than can be expected when themirror is separated from another reflective surface by more than severalwavelengths.

The method is illustrated in FIG. 3 at the right. Block 42 representsthe step in which the transmission through the mirrors a, b, in seriesis measured at a number of different degrees of separation from X to XThe task is to extrapolate to determine the value of T when the distanced equals 0. This can be done by computation or it can be done byplotting the data gathered in step 42 on a graph whose coordinates are Tand d. Measurements are taken to a very small value or separation. Therate of change of slope of the curve is measured in the vicinity of thatpoint and the curve extended to zero separation with a correspondingrate of change of slope. Intersection of the locus of graph points withthe d 0 line is identified and stored. The plotting method isillustrated in FIG. 3 by block 44 and the storage step at block 46.Computers and their peripheral apparatus are capable of practicing themethod either by use of the graphical or the computation step. However,the graphical method is simpler in the case of computation by hand andwhen hand methods are used to verify computer results. Accordingly, thegraphical method is preferred and is illustrated in FIG. 3.

Utilizing the value of T stored at block 24 and the value of T stored atblock 46, a computation is made at block 48 according to the solutionprogram instructions 300 which are applied at block 50 to controlcomputer operation at block 48. The output of that computation yieldsabsorption loss in mirrors a and b. The calculated values are stored asindicated in blocks 52 and 54, respectively. The information therestored is combined with total loss information for mirror a and formirror b which is stored in blocks 34 and 36, respectively. They arecombined to accomplish a computation, block 56, in accordance withsolution program 400 which has been stored at block 58. The result ofthe computation at step or block 58. The result of the computation atblock 56 is to subtract absorption loss from total loss in the twomirrors to find the quantities, scatter loss for mirror a and scatterloss for mirror b. These quantities are stored as indicated at steps 60and 62, respectively.

The solution program 300 is based on two considerations. First, sinceneither reflection nor transmission of light through the mirrors isaffected by the mirror spacing, the apparent difference between thetransmission when the mirrors are spaced and when they are not isaccounted for entirely by the fact that light, which is free to scatterwhen the mirrors are separated, cannot be scattered and must betransmitted when the spacing is zero. Hence, a scatter loss for the twomirrors is equal to the measured difference in transmission. It can bedemonstrated that the loss in the system thus determined is equal to theloss in each of the two mirrors.

Solution program 400 is simply a statement that the loss by scatter isthe difference between total loss and the loss by absorption.

FIG. 4 illustrates the steps involved in determining the loss in each ofthree mirrors. Steps 18, 20, 22, 24, 25, 26 and 23 of FIG. 3 describehow to determine and store information about the loss characteristic ofa pair of mirrors. Using those steps of the method of FIG. 3, the lossis determined and stored for each combination of the three mirrors takentwo at a time and the determination is stored as indicated in FIG. 4.The loss characteristic of mirror pair ab is stored in step 70 and theloss characteristic of mirror combination ac is stored at step 72.Finally, the loss characteristic of the combination of mirrors b and cis stored in step 74. The information stored in these steps is appliedto a computer which is controlled in step 76 by solution program 500.The computer solves, in step 78, for the loss in each mirror. The lossin mirror a is stored at step 80 whereas the loss in mirrors b and c arestored in steps 82 and 84, respectively. These losses, which wereconsidered to be equal for the several mirrors in establishing thecalculation procedure, are separately calculated at this step and anysmall difference is determined.

Referring to FIG. 10, the solution program 76 is simply a controlprogram to make the computer solve three equations by simultaneoussolution methods. Using this method, the loss components of the threemirrors can be separated working with the mirrors in pairs. Doing thatfor all three combinations of mirrors results in an expression that canbe solved simultaneously using solution program 500 and the methodillustrated at the right in FIG. 3.

An extension of the methods of FIG. 3 and FIG. 4 is illustrated in FIG.5. The method of that figure involves a computation step 86 which relieson a control step 88 in which the computation is controlled by asolution program 600 shown in detail in FIG. 11. The characteristics ofthree mirrors can be determined by measuring their individualtransmission characteristics and the transmission characteristic of allthree of them in series. The method can be used to determine thecharacteristics of three unknown mirrors. Ordinarily, however, themethod would be practiced using two mirrors whose characteristics wereknown. The embodiment of that method illustrated in FIG. 5 assumes thatmirrors a and b are specified and that their transmission had beendetermined and stored in steps 20 and 22 of the method of FIG. 3, andthat their reflectivity had been determined and stored in steps 38 and40 of FIG. 3. With that information available, mirrors a, b and c areplaced in series and their transmission characteristic measured. Also,mirror 0 has its transmission characteristic measured alone. All this isaccomplished in step 90 of FIG. 5. Information about the transmissioncharacteristic of mirror c is stored-at step 92 and information aboutthe transmission characteristics of all three mirrors in series isstored at step 94. Information about the characteristics Ra, Rb, Ta, Tb,Tc and Tube are fed into the computer for computation in step 86 underthe control of solution program 600 in a step 88. The computation yieldsthe value of loss in mirror 0 which is stored in a step 96.

That the solution program 600 can control the computer to calculate lossin mirror 3 can be demonstrated by examination and analysis of figures,the mirrors are illustrated by showing only their reflective surfaces.The substrates are omitted. FIG. 12 considers only that light fromsource p which bounces between the reflective coatings a and 0. FIG. 13considers only that light which bounces between reflective surfaces aand 0. Finally, FIG. 14 considers only that light that bounces betweenreflective surfaces b and c. There being no other light path through thesystem, these three figures describe the total possible light flow fromsource p through the three mirrors. That portion of the total lightwhich is accounted for in FIG. 12 is given by the following expression:

EXHIBIT B The light may bounce in such a manner as to give allcombinations at any transmission or reflection of all three kinds oflight flow. Accordingly, the expression for total light flow T is givenby the product:

T T T T EXHIBIT B Substitute: R l T oz The result of that substitutionyields an expression which can be solved by a reiterative process toyield the expression for loss in the third mirror which is the solutionprogram 600 of FIG. 11.

An apparatus suitable for practice of the method is illustrated inFIG. 1. An optical bench 100 includes a light source p and and opticalsystem 102 by which light can be directed toward mirrors a, b and c sothat light transmitted through those mirrors is collected and filteredin an optical system 104 and directed to a photomultiplier tube 106, theoutput of which is applied to a data storage unit 108. All of thestorage steps of the methods described above are accomplished in thatapparatus. Actual data storage can be on magnetic tape or in punchedcards or in any other conventional form by which it may be applied tothe computer 110. Output of the computer sends data back to the storageunit 108 for reuse in other steps. The programs 100, 200, 300, 400 and500 are stored in an apparatus 112 which has a form appropriate to theform of the computer 110. The program can be in the form of prewiredcircuit boards or in the form of punched cards which, by theirarrangement of holes, control the electrical behavior of the computer.The plotter l 14 is associated with the computer so that it can receiveits computations and make its extrapolation and return information tothe computer. The three mirrors a, b, and c are removable mounted uponsample holders 120, 122 and 124, respectively. The holders, and themirrors mounted upon them, are movable to change the spacing betweentheir respective reflective coatings.

I claim:

1. The method of determining the loss in mirrors which comprises thesteps of:

measuring the transmission through similar mirrors individually andmeasuring transmission through said mirrors in series with theirreflective surfaces spaced by more than a few wavelengths;

storing the measurements thus made;

computing the average loss of said mirrors using said storedmeasurements; and

computing the loss for each of said mirrors.

2. The invention defined in claim 1 which comprises the further step ofmeasuring the transmission through said mirrors in series at severaldifferent spacings;

extrapolating to find transmission through said mirrors at zero spacing;and

computing the average loss for said mirrors at zero spacing.

3. The method defined in claim 2 which comprises the further step ofdetermining scatter loss by subtracting the loss found when mirrorspacing was zero from the loss found when the mirrors were spaced.

4. The invention defined in claim 2 in which the extrapolation isaccomplished by plotting, finding the rate of change of the curveplotted as it approaches zero separation, extending the curve at thatrate of change to the point of zero separation; and

determining the magnitude of loss at the point at which the curvecrosses its zero separation point. 5. The method of finding the loss ina third mirror by using two mirrors which are similar to one another andwhose transmission and reflection characteristics are known, comprisingthe steps of:

measuring the transmission characteristic of the three mirrors inseries;

5 measuring the transmission characteristic of the third mirror; andusing the said known and measured characteristics,

computing the loss in said third mirror. 6. The invention defined inclaim 5 which comprises the further step of measuring averagetransmission characteristic through each pair of said three mirrors;

using said average transmission characteristic, solving for average lossin each of said pairs; and

using average transmission loss in each pair, solving simultaneously foractual loss in each mirror.

7. The method of ascertaining the loss characteristic in a test mirrorwhich comprises the step of measuring the transmission through the testmirror and two additional mirrors, and storing the measurements made;

measuring the transmission through all three mirrors and through allthree combinations of pairs of the mirrors at given spacing betweenmirrors and storing the measurements made; and

using the stored measurements and simultaneous equation solutionprocedures, solving for total loss in the test mirror.

8. The invention defined in claim 7 which comprises the further stepsof:

40 solving for total loss in said two additional mirrors;

measuring transmission through said pairs of mirrors at other spacings;

extrapolating to find transmission through each pair of mirrors at zerospacing;

solving for loss 1n the test mirror at zero spacing using theextrapolated values of transmission characteristic in simultaneousequation solution procedures. 9. Apparatus for determining the losscharacteristic of mirrors with the aid of a computer capable of solvingthe equations according to a solution program when furnished with inputdata, comprising:

a light source;

means for arranging at least two mirrors in series and individually inthe path of light emanating from said source;

means for measuring the quantity of light arriving at said mirrors andfor measuring the amount of that

1. The method of determining the loss in mirrors which comprises thesteps of: measuring the transmission through similar mirrorsindividually and measuring transmission through said mirrors in serieswith their reflective surfaces spaced by more than a few wavelengths;storing the measurements thus made; computing the average loss of saidmirrors using said stored measurements; and computing the loss for eachof said mirrors.
 2. The invention defined in claim 1 which comprises thefurther step of measuring the transmission through said mirrors inseries at several different spacings; extrapolating to find transmissionthrough said mirrors at zero spacing; and computing the average loss forsaid mirrors at zero spacing.
 3. The method defined in claim 2 whichcomprises the further step of determining scatter loss by subtractingthe loss found when mirror spacing was zero from the loss found when themirrors were spaced.
 4. The invention defined in claim 2 in which theextrapolation is accomplished by plotting, finding the rate of change ofthe curve plotted as it approaches zero separation, extending the curveat that rate of change to the point of zero separation; and determiningthe magnitude of loss at the point at which the curve crosses its zeroseparation point.
 5. The method of finding the loss in a third mirror byusing two mirrors which are similar to one another and whosetransmission and reflection characteristics are known, comprising thesteps of: measuring the transmission characteristic of the three mirrorsin sEries; measuring the transmission characteristic of the thirdmirror; and using the said known and measured characteristics, computingthe loss in said third mirror.
 6. The invention defined in claim 5 whichcomprises the further step of measuring average transmissioncharacteristic through each pair of said three mirrors; using saidaverage transmission characteristic, solving for average loss in each ofsaid pairs; and using average transmission loss in each pair, solvingsimultaneously for actual loss in each mirror.
 7. The method ofascertaining the loss characteristic in a test mirror which comprisesthe step of measuring the transmission through the test mirror and twoadditional mirrors, and storing the measurements made; measuring thetransmission through all three mirrors and through all threecombinations of pairs of the mirrors at given spacing between mirrorsand storing the measurements made; and using the stored measurements andsimultaneous equation solution procedures, solving for total loss in thetest mirror.
 8. The invention defined in claim 7 which comprises thefurther steps of: solving for total loss in said two additional mirrors;measuring transmission through said pairs of mirrors at other spacings;extrapolating to find transmission through each pair of mirrors at zerospacing; solving for loss in the test mirror at zero spacing using theextrapolated values of transmission characteristic in simultaneousequation solution procedures.
 9. Apparatus for determining the losscharacteristic of mirrors with the aid of a computer capable of solvingthe equations according to a solution program when furnished with inputdata, comprising: a light source; means for arranging at least twomirrors in series and individually in the path of light emanating fromsaid source; means for measuring the quantity of light arriving at saidmirrors and for measuring the amount of that light that is transmittedthrough mirrors arranged in said path; and means for storing themeasurements made.
 10. The invention defined in claim 9 which furthercomprises means for extrapolating plotted data including means capableof drawing the curve of transmission characteristic against mirrorseparation between measured data points; said means for extrapolatingplotted data further including means for extending the curve to zeroseparation and determining the plotted value of transmissioncharacteristics at zero separation.